6. A sphere of radius R2 has a concentric central cavity of radius R1. The material between R1 and R2 has thermal conductivity k. Radius R2 is maintained at temperature T2, and radius Ri is maintained at temperature T1. Find the rate of heat flow across any spherical surface within the spherical shell. Hint: the rate of heat flow is the same for all such surfaces (why?), and remember that the area of a spherical surface depends on the radius.

6. A sphere of radius R2 has a concentric central cavity of radius R1. The material between R1 and R2 has thermal conductivity k. Radius R2 is maintained at temperature T2, and radius Ri is maintained at temperature T1. Find the rate of heat flow across any spherical surface within the spherical shell. Hint: the rate of heat flow is the same for all such surfaces (why?), and remember that the area of a spherical surface depends on the radius.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.3P: 1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of...

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2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.
1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.
Calculate the heat transferred from the cube-shaped iron mass (a = 30 cm) to the environment at 20 ° C with all surfaces at a temperature of 100 ° C. (Assume that the heat is only from the surfaces, the inner parts of the surfaces are insulated.)
A small sphere (emissivity =0.503 radius=r1) is located at the center of a spherical abestos shell ( thickness =1.74 cm, outer radius= r2; thermal conductivity of abestos is 0.090 J/ (sm c degrees) The thickness of the shell is small compared to the inner and outer radii of the shell. The temperature of the small sphere is 695 degrees Celsius while the temperature of the inner surface of the shell is 352 degrees Celsius, both temperatures remaining constant. Assuming that r2/r1 =8.75 and ignoring any air inside the shell, find the temperature in degrees Celsius of the outer surface of the shell.
An electric heating system is installed in the ceiling of a room 5 m (length) × 5 m (width) ×2.5 m (height). The temperature of the ceiling is 315 K whereas under equilibrium conditions the walls are at 295 K. If the floor is non-sensitive to radiations and the emissivities of the ceiling and wall are 0.75 and 0.65, respectively. Calculate the radiant heat loss from the ceiling to the walls. The answer should be 1595 W. Please show steps in your solution
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Sputnik 1, the first satellite launched into space by the Russians in 1957, is a 2-shell aluminum alloy (2024-T6) sphere. The highly polished outer shell (seeing deep space) is 585 mm in diameter, and has thickness of 1 mm (ID = 583 mm). The inside shell is 2 mm thick. There is a contact resistance between the two aluminum shells of value Rc"= 200 m2·K/W. Inside the shell, there is a radio unit that is uniformly dissipating thermal energy of Qradio = 1 W. Determine the steady-state temperature on the inner shell’s inner wall (ignore the effects of the antennas). Hint: You can use a radiation heat transfer coefficient hr = εσTshell3
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A sphere of radioactive material of radius aR is wrapped with a ceramic casing of outer radius R.The heat flux density emitted by the sphere radioactive on its surface is qaR. Find the temperature profile of the spherical shell if the thermal conductivity of the housing material varieswith its radius according to k = Kr (where K is a constant and r is the distance from the center of thesphere) and the temperature outside the casing is keeps T constant R